from itertools import combinations


class dsu:
    n = 1
    parent_or_size = [-1 for i in range(n)]

    def __init__(self, N):
        self.n = N
        self.parent_or_size = [-1 for i in range(N)]

    def merge(self, a, b):
        assert 0 <= a < self.n, "0<=a<n,a={0},n={1}".format(a, self.n)
        assert 0 <= b < self.n, "0<=b<n,b={0},n={1}".format(b, self.n)
        x = self.leader(a)
        y = self.leader(b)
        if x == y:
            return x
        if -self.parent_or_size[x] < -self.parent_or_size[y]:
            x, y = y, x
        self.parent_or_size[x] += self.parent_or_size[y]
        self.parent_or_size[y] = x
        return x

    def same(self, a, b):
        assert 0 <= a < self.n, "0<=a<n,a={0},n={1}".format(a, self.n)
        assert 0 <= b < self.n, "0<=b<n,b={0},n={1}".format(b, self.n)
        return self.leader(a) == self.leader(b)

    def leader(self, a):
        assert 0 <= a < self.n, "0<=a<n,a={0},n={1}".format(a, self.n)
        if self.parent_or_size[a] < 0:
            return a
        self.parent_or_size[a] = self.leader(self.parent_or_size[a])
        return self.parent_or_size[a]

    def size(self, a):
        assert 0 <= a < self.n, "0<=a<n,a={0},n={1}".format(a, self.n)
        return -self.parent_or_size[self.leader(a)]

    def groups(self):
        leader_buf = [0 for i in range(self.n)]
        group_size = [0 for i in range(self.n)]
        for i in range(self.n):
            leader_buf[i] = self.leader(i)
            group_size[leader_buf[i]] += 1
        result = [[] for i in range(self.n)]
        for i in range(self.n):
            result[leader_buf[i]].append(i)
        result2 = []
        for i in range(self.n):
            if len(result[i]) > 0:
                result2.append(result[i])
        return result2


WAYS = [(1, 0), (-1, 0), (0, 1), (0, -1)]


def solve():
    N, K = map(int, input().split())

    for comb in combinations(range(N**2), K):
        comb_set = set(comb)

        uf = dsu(N**2)
        empty = set()

        for x in comb:
            i, j = x // N, x % N

            for di, dj in WAYS:
                ni, nj = i + di, j + dj
                nx = ni * N + nj

                if not (0 <= ni < N and 0 <= nj < N):
                    continue

                if nx in comb_set:
                    uf.merge(x, nx)
                else:
                    empty.add(nx)

        if uf.size(comb[0]) != K:
            continue

        if len(empty) != K:
            continue

        print("Yes")
        for i in range(N):
            for j in range(N):
                if i * N + j in comb:
                    print("#", end="")
                else:
                    print(".", end="")
            print()
        return

    print("No")


if __name__ == "__main__":
    T = int(input())
    for _ in range(T):
        solve()